code: def lpmin(f, constr):
      """return minimum of linear equation ``f`` under
      linear constraints expressed using Ge, Le or Eq.
  
      All variables are unbounded unless constrained.
  
      Examples
      ========
  
      >>> from sympy.solvers.simplex import lpmin
      >>> from sympy import Eq
      >>> from sympy.abc import x, y
      >>> lpmin(x, [2*x - 3*y >= -1, Eq(x + 3*y, 2), x <= 2*y])
      (1/3, {x: 1/3, y: 5/9})
  
      Negative values for variables are permitted unless explicitly
      exluding, so minimizing ``x`` for ``x <= 3`` is an
      unbounded problem while the following has a bounded solution:
  
      >>> lpmin(x, [x >= 0, x <= 3])
      (0, {x: 0})
  
      Without indicating that ``x`` is nonnegative, there
      is no minimum for this objective:
  
      >>> lpmin(x, [x <= 3])
      Traceback (most recent call last):
      ...
      sympy.solvers.simplex.UnboundedLPError:
      Objective function can assume arbitrarily large values!
  
      See Also
      ========
      linprog, lpmax
      """
      return _lp(min, f, constr)
  
imports: from sympy.core import sympify
  from sympy.core.exprtools import factor_terms
  from sympy.core.relational import Le, Ge, Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy
  from sympy.core.sorting import ordered
  from sympy.functions.elementary.complexes import sign
  from sympy.matrices.dense import Matrix, zeros
  from sympy.solvers.solveset import linear_eq_to_matrix
  from sympy.utilities.iterables import numbered_symbols
  from sympy.utilities.misc import filldedent
label_desc: Use image node_id 10 for calling a global function with example usage: lpmin(f, constr) and returns: _lp